Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Objects transiting near or within the disruption radius of both main-sequence (e.g. KOI 1843) and white dwarf (WD 1145+017) stars are now known. Upon fragmentation or disintegration, these planets or asteroids may produce co-orbital configurations of nearly equal mass objects. However, as evidenced by the co-orbital objects detected by transit photometry in the WD 1145+017 system, these bodies are largely unconstrained in size, mass, and total number (multiplicity). Motivated by potential future similar discoveries, we perform N-body simulations to demonstrate if and how debris masses and multiplicity may be bounded due to second-to-minute deviations and the resulting accumulated phase shifts in the osculating orbital period amongst multiple co-orbital equal point masses. We establish robust lower and upper mass bounds as a function of orbital period deviation, but find the constraints on multiplicity to be weak. We also quantify the fuzzy instability boundary, and show that mutual collisions occur in less than 5, 10, and 20 per cent of our simulations for masses of 10(21), 10(22), and 10(23) kg. Our results may provide useful initial rough constraints on other stellar systems with multiple co-orbital bodies.